Miller cylindrical projection

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A Miller projection of the Earth. Miller projection SW.jpg
A Miller projection of the Earth.
Miller projection with 1,000 km indicatrices of distortion. Miller with Tissot's Indicatrices of Distortion.svg
Miller projection with 1,000 km indicatrices of distortion.

The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 45, projected according to Mercator, and then the result is multiplied by 54 to retain scale along the equator. [1] Hence:

Contents

or inversely,

where λ is the longitude from the central meridian of the projection, and φ is the latitude. [2] Meridians are thus about 0.733 the length of the equator.

In GIS applications, this projection is known as: "ESRI:54003 - World Miller Cylindrical" [3]

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees. [4]

See also

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Bottomley projection

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Universal Transverse Mercator coordinate system coordinate system

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Lambert conformal conic projection map projection

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Space-oblique Mercator projection map projection

Space-oblique Mercator projection is a map projection devised in the 1970s for preparing maps from Earth-survey satellite data. It is a generalization of the oblique Mercator projection that incorporates the time evolution of a given satellite gound track to optimize its representation on the map. The oblique Mercator projection, on the other hand, optimizes for a given geodesic.

Cassini projection map projection

The Cassini projection is a map projection described by César-François Cassini de Thury in 1745. It is the transverse aspect of the equirectangular projection, in that the globe is first rotated so the central meridian becomes the "equator", and then the normal equirectangular projection is applied. Considering the earth as a sphere, the projection is composed of the operations:

Wagner VI projection

Wagner VI is a pseudocylindrical whole Earth map projection. Like the Robinson projection, it is a compromise projection, not having any special attributes other than a pleasing, low distortion appearance. Wagner VI is equivalent to the Kavrayskiy VII horizontally elongated by a factor of ​. This elongation results in proper preservation of shapes near the equator but slightly more distortion overall. The aspect ratio of this projection is 2:1, as formed by the ratio of the equator to the central meridian. This matches the ratio of Earth’s equator to any meridian.

Cylindrical equal-area projection

In cartography, the cylindrical equal-area projection is a family of cylindrical, equal-area map projections.

Eckert IV projection

The Eckert IV projection is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. In each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert IV is the Eckert III projection.

Eckert II projection

The Eckert II projection is an equal-area pseudocylindrical map projection. In the equatorial aspect the network of longitude and latitude lines consists solely of straight lines, and the outer boundary has the distinctive shape of an elongated hexagon. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert II is the Eckert I projection.

Central cylindrical projection

The central cylindrical projection is a perspective cylindrical map projection. It corresponds to projecting the Earth's surface onto a cylinder tangent to the equator as if from a light source at Earth's center. The cylinder is then cut along one of the projected meridians and unrolled into a flat map.

Gall stereographic projection Cylindrical map projection

The Gall stereographic projection, presented by James Gall in 1855, is a cylindrical projection. It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection.

Web Mercator projection Mercator projection variant

Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator or WGS 84/Pseudo-Mercator is a variant of the Mercator projection and is the de facto standard for Web mapping applications. It rose to prominence when Google Maps adopted it in 2005. It is used by virtually all major online map providers, including Google Maps, Mapbox, Bing Maps, OpenStreetMap, Mapquest, Esri, and many others. Its official EPSG identifier is EPSG:3857, although others have been used historically.

Rectangular polyconic projection

The rectangular polyconic projection is a map projection was first mentioned in 1853 by the U.S. Coast Survey, where it was developed and used for portions of the U.S. exceeding about one square degree. It belongs to the polyconic projection class, which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Sometimes the rectangular polyconic is called the War Office projection due to its use by the British War Office for topographic maps. It is not used much these days, with practically all military grid systems having moved onto conformal projection systems, typically modeled on the transverse Mercator projection.

References

  1. Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, ISBN   0-226-76747-7.
  2. "Miller Cylindrical Projection". Wolfram MathWorld. Retrieved 25 March 2015.
  3. "Projected coordinate systems". ArcGIS Resources: ArcGIS Rest API. ESRI. Retrieved 16 June 2017.
  4. http://cartographicperspectives.org/index.php/journal/article/view/cp78-patterson-et-al/1362